Acoustic filtering and guiding by the presence of a defect at the opened resonators level’s in one-dimensional comb-like phononic structure

Abstract

In this work, we theoretically study the existence of defect modes, which can be used for acoustic waves filtering and guiding applications at ultra-fine frequencies; in the case of a comb-like periodic structure containing P defects at the opened resonators level. The perfect phononic structure consists of a finite segment of length d1 which along a lateral branch (plays the role of the resonator) of height d2 is grafted on each site. The numerical results plotted from the analytical equations show the existence of pass bands separated by large band gaps in which the acoustic waves are prohibited to propagate. These gaps come from the periodicity of the system at each segment of length d1 and the resonant modes of the lateral branches of height d2. Our theoretical analysis is performed employing the continuous Media Interface Response method based on the Green function approach, which allows us to deduce the physical properties of any composite structures, in particular, the dispersion relation, the transmission coefficient, the phase time and the group velocity. Moreover, we examine the effect of the introduction of defects at the opened resonators located inside the ideal comb-like periodic structure. The presence of a defect in this structure gives rise to localized phononic states (defect modes) created at particular frequencies, called filtered frequencies, situated inside the wide band gaps. These filtered frequencies are extremely sensitive to the number of cells N, the number P of the branched defective resonators, the position J of defect, and the height of defect d02. Acoustic waves can be conducted for a vast range of applications, in particular, the manufacture of filtering devices, waveguiding, sensor, noise reduction, and improvement of acoustic attenuation performance.

Topics & Concepts